1. For the sake of simplicity, we'll use this image of Ye Eun of the Wonder Girls with a clean, white background.

2. Duplicate this layer. On the bottom layer, create a layer mask (second button at the bottom of your layer palette) and fill it with black.

3. Go back to the top layer. Go to Filter > Extract and a window should pop up. Click here for image. You can adjust the brush size depending on how big your image is. Generally, I leave it as 10px. Grab the edge highlighter tool (at the top left) and trace around your subject. As you can see, I also traced around the hook of her arm because I want that part erased, too. Remember not to leave any open spaces in the trace line you are making around her. After you're done, select the paint bucket and click on the subject. She should now be entirely purple. Press okay.

4. This is what you have now:

5. From afar, it looks like you're done already. But add two layers at the very bottom of the layer palette and fill one with a dark color and one with a light color. You will see that there are parts of her that has accidentally been erased! This is because parts of her clothing are also light, so when you were tracing around her before, the extract tool also picked up parts of her clothing that blended in with the white background.

6. There are two things we have to fix now: parts that were supposed to be erased but the extracter tool did not pick it up, and parts that were NOT supposed to be erased but were. Let's fix the first problem first. Create a layer mask in the extracted layer but do not fill it. Grab a very small (3-5px) BLACK hard round brush. On the layer mask, I erased the tiny white part at the top of her head that's not supposed to be there.

*Another thing: what's the purpose of the two layers I told you to create in step 5? This is so you can see how the cutout image will look against a light or dark background. Also, you can easily see which parts need to be fixed when you have a non-transparent background. You can switch between the dark and light layers simply by clicking the icon that looks like an eye next to one of the layers to hdie it.

7. Now for the parts that were NOT supposed to be erased. Go to the non-extracted layer where you have a layer mask filled entirely in black. This time, you grab a WHITE hard round brush and go over the parts that were not supposed to be erased. Switch between brush sizes depending on which part of her body you are working on and feel free to go back from black brush to white brush if you've made a mistake by perssing X on your keyboard.

8. When you're done, delete the two dark and light layers and then go to Layer > Merge Visible. Go to File > Save As and for the format, select PNG. Do NOT save it as a JPG or your won't have your transparent background. Now free to slap the image on any background you like. =)